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hyperbolic dynamical systems

Journal of the Institute of Mathematics of Jussieu (1)

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PERTURBATION OF THE SEMICLASSICAL SCHRÖDINGER EQUATION ON NEGATIVELY CURVED SURFACES
Part of
Suresh Eswarathasan, Gabriel Rivière
Journal:

Journal of the Institute of Mathematics of Jussieu / Volume 16 / Issue 4 / September 2017

Published online by Cambridge University Press:

27 August 2015, pp. 787-835

Print publication:

September 2017
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We consider the semiclassical Schrödinger equation on a compact negatively curved surface. For any sequence of initial data microlocalized on the unit cotangent bundle, we look at the quantum evolution (below the Ehrenfest time) under small perturbations of the Schrödinger equation, and we prove that, in the semiclassical limit, and for typical perturbations, the solutions become equidistributed on the unit cotangent bundle.